A265136 Numbers that are the sum of two distinct nonzero triangular numbers in exactly three ways.

81, 106, 181, 211, 256, 276, 331, 361, 381, 406, 456, 556, 606, 631, 666, 681, 706, 718, 731, 781, 856, 861, 931, 939, 956, 981, 1051, 1131, 1206, 1231, 1456, 1506, 1563, 1606, 1631, 1681, 1731, 1732, 1756, 1831, 1891, 1901, 1956, 1981, 2081, 2095, 2101

Offset

1,1

Links

Table of n, a(n) for n=1..47.

Mathematica

r = 2101; lst = Table[0, {r}]; lim = Floor[Sqrt[8*r - 7]]; Do[num = (i^2 + i)/2 + (j^2 + j)/2; If[num <= r, lst[[num]]++], {i, lim}, {j, i - 1}]; Flatten@Position[lst, 3]
Module[{nn=70, trnos}, trnos=Accumulate[Range[nn]]; Select[ PositionIndex[ Sort[ Counts[Total/@Subsets[trnos, {2}]]]][3], #<=Last[trnos]&]] (* The program uses the PositionIndex and Counts functions from Mathematica version 10 *) (* Harvey P. Dale, Dec 25 2015 *)

Crossrefs

Cf. A000217, A051533, A260647, A265140 (exactly one way), A262749 (more than one way), A265134 (exactly two ways), A265135 (more than two ways), A265137 (more than three ways), A265138 (exactly four ways).

Sequence in context: A249613 A064828 A265135 * A120457 A129151 A039546

Adjacent sequences: A265133 A265134 A265135 * A265137 A265138 A265139

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved